Question: Solve for $x$ : $ 3|x + 10| + 8 = 6|x + 10| + 9 $
Explanation: Subtract $ {3|x + 10|} $ from both sides: $ \begin{eqnarray} 3|x + 10| + 8 &=& 6|x + 10| + 9 \\ \\ {- 3|x + 10|} && {- 3|x + 10|} \\ \\ 8 &=& 3|x + 10| + 9 \end{eqnarray} $ Subtract $9$ from both sides: $ \begin{eqnarray} 8 &=& 3|x + 10| + 9 \\ \\ {- 9} && {- 9} \\ \\ -1 &=& 3|x + 10| \end{eqnarray} $ Divide both sides by ${3}$ $ \dfrac{-1} {{3}} = \dfrac{3|x + 10|} {{3}} $ Simplify: $ -\dfrac{1}{3} = |x + 10| $ The absolute value cannot be negative. Therefore, there is no solution.